Black scholes option pricing model

A pricing model that ranks among the most influential. It was devised by Fischer Black and Myron Scholes, two Chicago academics, in 1973, the year that formalized options trading began on the Chicago board of trade. The Black-Scholes model, or adaptations of it, has gained universal acceptance for pricing options because its results are almost as good as those achieved by other options pricing models without the complexity.

Behind the model is the assumption that asset prices must adjust to prevent arbitrage between various combinations of options and cash on the one hand and the actual asset on the other. Additionally, there are specific minimum and maximum values for an option which are easily observable. Assuming, for example, that it is a call option then its maximum value must be the share price. Even if the exercise price is zero, no one will pay more than the share price simply to acquire the right to buy the shares. The minimum value, meanwhile, will be the difference between the share's price and the option's exercise price adjusted to its present value.

The model puts these fairly easy assumptions into a formula and then adjusts it to account for other relevant factors.

• The cost of money, because buying an option instead of the underlying stock saves money and, therefore, makes the option increasingly valuable the higher interest rates go.
• The time until the option expires, because the longer the period, the more valuable the option becomes since the option holder has more time in which to make a profit.
• The volatility of the underlying share price, because the more it is likely to bounce around, the greater chance the option holder has to make a profit.

Of these, volatility, as measured by the standard deviation of share returns, is the most significant factor. Yet it was the factor over which Black and Scholes struggled because it is not intuitively obvious that greater volatility should equal greater value. That it is so is because of the peculiar nature of options: they peg losses to the amount paid for the option, yet they offer unlimited potential for profit.

Note that the basic Black-Scholes model is for pricing a call option, but it can be readily adapted for pricing a put option. It also ignores the effect on the price of the option of any dividends that are paid on the shares during the period until the option expires. This is remedied either by deducting the likely present value of any dividend from the share price that is input into the model, or by using a refinement of the Black-Scholes model which writes off the effect of the dividend evenly over the period until it is paid.